𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Invariant Sobolev Calculus on the Free Loop Space

✍ Scribed by R. Leandre


Book ID
110228673
Publisher
Springer Netherlands
Year
1997
Tongue
English
Weight
649 KB
Volume
46
Category
Article
ISSN
0167-8019

No coin nor oath required. For personal study only.


πŸ“œ SIMILAR VOLUMES


Integration by parts formulas and rotati
✍ R. Leandre πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 606 KB

We give formulas for integration by parts over the path space and over the loop space of a manifold. We define Sobolev spaces and an Ornstein-Uhlenbeck operator on the loop space. We find some functionals which belongto all the Sobolev spaces.

Logarithmic Sobolev Inequality on Free L
✍ Yuzuru Inahama πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 286 KB

In this paper we will prove the logarithmic Sobolev inequality on free loop groups for various heat kernel measures which P. Malliavin (1989Malliavin ( , 1991, in ``Diffusion Process and Related Problems in Analysis (M. A. Pinsley, Ed.), Vol. I, Birkha user, Basel) constructed. Those measures are as

PoincarΓ© Inequality for Weighted First O
✍ Fuzhou Gong; Michael RΓΆckner; Wu Liming πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 268 KB

Taking lim sup L Γ„ lim k Γ„ in both sides of (2.10), by (i), (2.8), (2.9), and the fact that lim k Γ„ \* k =1 we get a contradiction. Hence, , is not identically zero.

The Log-Sobolev Inequality on Loop Space
✍ Fu-Zhou Gong; Zhi-Ming Ma πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 371 KB

We obtain a log-Sobolev inequality with a neat and explicit potential for the gradient on a based loop space over a compact Riemannian manifold. The potential term relies only on the curvature of the manifold and the Hessian of the heat kernel, and is L p -integrable for all p 1. The log-Sobolev ine